Thermonuclear burst oscillations and ocean waves

Accreting neutron stars can exhibit high-frequency modulations in their lightcurves during thermonuclear X-ray bursts, known as burst oscillations. These frequencies can be offset from the neutron star spin frequency by several Hz (where known independently) and can drift by 1-3 Hz. One plausible explanation for these observations is that a wave is present in the bursting ocean, the rotating frame frequency of which is the offset from the neutron star spin frequency. As the ocean cools in the aftermath of the burst, the frequency of the wave should decrease (in the rotating frame) hence explaining the drift. A strong candidate to explain this phenomenon is a buoyant r-mode. Before this thesis, models that accounted for the radial structure of these modes neglected the burning of nuclear fuel in the tail of the burst as well as relativistic effects. These previous models over-predicted the frequency drifts and frequency offset. Using burst models that include the burning of nuclear fuel, the evolution of the buoyant r-mode is calculated and the resulting frequency drifts are smaller. Including frame-dragging and gravitational redshift reduces the frequency drift and the rotating frame frequency. This thesis also calculates the frequency of a buoyant r-mode at the ocean-crust interface of a neutron star during a superburst. Such bursts can last hours and are caused by burning carbon unstably. It is shown that the frequency evolution of the r-mode is not consistent with the sole observation of oscillation during a superburst observed on 4U-1636-536.